# Strong Euler Wellcomposedness

## Abstract

In this paper, we define a new flavour of well-composedness, called strong Euler well-composedness. In the general setting of regular cell complexes, a regular cell complex of dimension ${\displaystyle n}$ is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is ${\displaystyle 1}$, which is the Euler characteristic of an ${\displaystyle (n-1)}$-dimensional ball. Working in the particular setting of cubical complexes canonically associated with ${\displaystyle n}$-D pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension ${\displaystyle n\geq 2}$ and that the converse is not true when ${\displaystyle n\geq 4}$.

## Bibtex (lrde.bib)

```@Article{	  boutry.21.joco,
author	= {Nicolas Boutry and Rocio Gonzalez-Diaz and Maria-Jose
Jimenez and Eduardo Paluzo-Hildago},
title		= {Strong {E}uler Wellcomposedness},
journal	= {Journal of Combinatorial Optimization},
month		= nov,
year		= {2021},
abstract	= {In this paper, we define a new flavour of
well-composedness, called strong Euler well-composedness.
In the general setting of regular cell complexes, a regular
cell complex of dimension \$n\$ is strongly Euler
well-composed if the Euler characteristic of the link of
each boundary cell is \$1\$, which is the Euler
characteristic of an \$(n-1)\$-dimensional ball. Working in
the particular setting of cubical complexes canonically
associated with \$n\$-D pictures, we formally prove in this
paper that strong Euler well-composedness implies digital
well-composedness in any dimension \$n\geq 2\$ and that the
converse is not true when \$n\geq 4\$.},
doi		= {10.1007/s10878-021-00837-8}
}```